INTERFERENCE OF POLARIZED LIGHT. 



responding tints is, however, much greater in crystalline plates 

 exposed to polarized light, than in thin plates of air, or any 

 other uniform medium. The black of the first order appears 

 in a plate of sulphate of lime, when the thickness is the 

 2 oV oth of an inch. Between 2^0 o^ n an( ^- jV^ n ^ an i ncn > we 

 have the whole succession of colours of Newton's scale ; and 

 when the thickness exceeds the latter limit, the transmitted 

 light is always white. The tint produced by a plate of mica, 

 in polarized light, is the same as that reflected from a plate 

 of air of only the ^J n th part of the thickness. 



Pursuing the examination of the same subject for oblique 

 incidences, M. Biot found that, in uniaxal crystals, the tint 

 developed or rather the number of periods and parts of a 

 period belonging to a ray of given refrangibility was deter- 

 mined by the length of the path traversed by the light within 

 the crystal, and by the square of the sine of the angle which 

 its direction made with the optic axis, jointly. In biaxal 

 crystals we must substitute, for the square of the sine, the 

 product of the sines of the angles which the ray makes with 

 the two axes. 



(228) Let us now turn to the physical theory, and see in 

 what manner it explains the appearances. 



We have seen that the wave incident upon a crystal 

 is resolved into two sets of waves within it, which traverse 

 it in different directions, and with different velocities. One 

 of these waves, therefore, will lag behind the other, and they 

 will be in different phases of vibration at emergence. When 

 the plate is thin, this retardation of one wave upon the other 

 will amount only to a few undulations and parts of an undu- 

 lation ; and it would therefore appear that we have here all 

 the conditions necessary for their interference, and the con- 

 sequent production of colour. 



But here we are met by a difficulty. So far as this expla- 



